Formula:3971

Digital Library of Mathematical Functions ID 10.20.E17

${\displaystyle{\displaystyle z=\pm(\tau\coth\tau-\tau^{2})^{\frac{1}{2}}\pm\mathrm{i}(\tau^{2}-\tau\tanh\tau)^{\frac{1}{2}},}}$

Constraint(s)

${\displaystyle{\displaystyle 0\leq\tau\leq\tau_{0}}}$

Symbols List

• ${\displaystyle{\displaystyle\coth\NVar{z}}}$: hyperbolic cotangent function
• ${\displaystyle{\displaystyle\tanh\NVar{z}}}$: hyperbolic tangent function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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